Abstract Algebra has its origins in the number theory of antiquity, and arose as a subject in the late 18th Century as a tool to help to understand the zeroes of polynomials. From these origins, it has grown mightily and now it pervades much of modern pure mathematics. Curiously, this formerly purest of pure disciplines has become rather practical. Simply put, abstract algebra underlies the security and integrity of all modern digital communication.

    Our course is not about the uses of abstract algebra in digital communication. Its goal is to introduce you to the mathematical methods of inquiry (definition, conjecture, and proof), and train you in the rigor of thought that is unique to mathematics. We will build on my 411 course, which dealt with groups. Our first topic will be rings, which are generalizations of the integers and where one studies solutions to polynomials. We will finish the course by studying fields, including finite fields.

    A key role in this course will be played by your homework, which will serve as a dialog between us. The exact schedule of homework will depend upon arrangement I make with our grader, who has not yet been selected. Some guidelines though are set. Homework will be assigned regularly and late homework is not accepted. Homework will be graded and returned promptly. Your homework write ups are expected to represent your own work and should be carefully and neatly written. An important part of your education is learning from your peers. I encourage you to discuss problems with others in the class, but the problem write ups must be your own (n identical solutions will each receive 1/n of the credit).

    The key component of careful thought is recognizing and communicating correct arguments, while avoiding false statements. Accordingly, full credit will be given for well-written, correct solutions that are unblemished by false assertions.

    Abstract Algebra, like other advanced mathematics courses requires students to be engaged in classroom discourse. To encourage class participation, good questions will be rewarded with specially prepared coupons (on post-it notes), which may be redeemed for extra credit (1/2 of a homework assignment).

    I will have three office hours scheduled each week. Appointments may be made, as well. The most reliable way to contact me is via email - I read and respond to it whenever I am in my office.

    Due to my having to apply for jobs and some professional committments, there will be several class periods that will be taught by substitutes, and we may have to reschedule one or more classes. I ask your patience with this, especially in the first few weeks of the course.